Should I play again on a new account?

I made a new account months ago, and I don't regret it, had a lot of luck summoning. However, you already have good units, as Ayra, Elincia, B!Lyn and a Nowi -why keeping her 4 stars?- you have no guarantee getting once more. So keep that account (linked?) and you can try making a new one on another device.
For a team, I'd go with Ayra/Siegbert; Lissa; Ninian and B!Lyn. And if you want to go with horse emblem, my actual team is Siegbert B!Lyn Reinhardt and Camus(you can replace him by Titania to soak magic), so if your Rein has a good IV, then you know what to do

Quick tip, get as many characters to level 40 even if they're 4 stars. Chain Challenges can be easy when you have options. I wouldn't recommend making a new account. Just work with what you got. Feathers are easy to come by so making 5 star units can be done quickly

No. Creating new account is the worst solution if it's about Chain Challenge. You'll need quantity instead of quality for it. Team composition is also important, but horse team should do fine for Lunatic 1-10.
As for second team, you can go
1. Tharja, Eirika, Ninian, Fae revolving around Thaja blade tome. Eirika as buffer & Fae as blue check
2. Ayra, Fjorm, Winter Chrom & Winter Liz
3. Elincia, Clair, Camilla, 4* Subaki

Not to mention Celica & Julia is also a strong unit

No point in making a new account with all those amazing units.The only thing you are lacking is blue units,but it can be worked out.

I think your team's rly good tho, it would be a waste to just throw em away. Like some of the guys here said, I recommend raising those 4* units to Lv. 40. If you're still struggling with the chain challenges, you can look for references in youtube (or maybe other sites like gamefaqs idk lol), and then formulate your team creatively. It's the process on things like these that rly made this game counts lmao